Massachusetts Institute of Technology - Physics Department
Physics - 8.01 Assignment #7 November 1, 1999.
It is st ron gl y reco mm en ded that you read about a subject bef ore it is covered in lectures.
Lecture Date Material Covered Reading
#21 Mon 11/1 Torques - Oscillating Bodies - Hoops Page 325 – 334, 394 – 396
#22 Wed 11/3 Kepler’s Laws - Elliptical Orbits Page 218 – 229
Satellites - Change of Orbits - Ham Sandwich Lecture Supplement of 11/3
See the Home Page
#23 Fri 11/5 Doppler Effect - Binary Stars Page 446 – 450
Neutron Stars and Black Holes Take Notes!
#24 Mon 11/8 Rolling Motion - Gyroscopes Page 335 – 336, 339 – 345
Very Non-Intuitive! Lecture Supplement of 11/8
See the Home Page
Due Monday, Nov 8, before 4 PM in 4-339B.
This is not an easy assignment; start early!
7.1 Multiple-Stage Rocket – page 271, problem 55
7.2 Slingshot Encounters
Spacecrafts can gain in mechanical energy as they encounter a planet. This may appear as a violation
of the conservation of mechanical energy, but it is not. The gained energy is at the expense of the
orbital energy of the planet. The easiest way to see how this works in principle is to treat the problem
as a one-dimensional collision. Let the spacecraft have a mass mand just before the encounter a
velocity v, the planet a mass Mand velocity V. Both velocities are relative to the sun and they
are in opposite directions. Thus the angle between vand Vis 180◦. Assume that the spacecraft
rounds the planet and departs in the opposite direction. Thus, after the encounter the velocity of
the spacecraft is in the same direction as V.
a) What is the speed of the spacecraft after the encounter in terms of m,Mand the speed of the
spacecraft before the encounter and the speed of the planet before the encounter?
b) The speed of the spacecraft just before the encounter is 10 km/sec and the speed of the planet
13 km/sec (this is the orbital speed of Jupiter). What then is the speed of the spacecraft just
after the encounter?
c) If the spacecraft has a mass of 2000 kg, by how much has its energy increased?
7.3 Figure Skater – page 320, problem 23
7.4 Paral lel Ax is Theorem – page 320, problem 26 PIVoT
7.5 Pulsars – page 322, problem 41
7.6 Perpendicular Axis Theorem – page 322, problem 45 PIVoT
7.7 Change of Angular Momentum due to a Torque – page 324, problem 59 PIVoT
7.8 Spin Up of Disk due to a Torque – page 348, problem 11 PIVoT
